Given a complex number #z = a+bi#, the complex conjugate of #z#, denoted #bar(z)#, is #bar(z) = a-bi#. For any complex number, #zbar(z)# is a real number. Thus, we can eliminate the complex number from the denominator by multiplying the numerator and the denominator by the conjugate of the denominator.
#(4+5i)/(2-3i) = ((4+5i)(2+3i))/((2-3i)(2+3i))#
#=(-7+22i)/13#
#=-7/13+22/13i#